On Huang and Noor's Open Problem

TL;DR

This paper proposes a new iterative algorithm for variational inclusions with H-monotone operators, proving its strong convergence and convergence rate, thereby addressing an open problem posed by Huang and Noor in 2007.

Contribution

It introduces and analyzes a novel iterative method with proven convergence properties for a specific class of variational inclusions involving H-monotone operators.

Findings

Proved strong convergence of the new algorithm.

Provided convergence rate estimates.

Addressed an open problem by Huang and Noor.

Abstract

In this paper, we introduce and analyze a new iterative algorithm for solving a class of variational inclusions involving H-monotone operators. The strong convergence of this algorithm is proved and estimate of its convergence rate is supplied as an answer to an open question posed by Huang and Noor [Huang, Z., Noor, M. A. (2007). Equivalency of convergence between one-step iteration algorithm and two-step iteration algorithm of variational inclusions for H-monotone mappings. Computers & Mathematics with Applications, 53(10), 1567-1571.].